This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Learning Target• Understand that shapes in different
categories may share attributes, and that the shared attributes can define a larger category. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.
SMP 1, 2, 3, 4, 5, 6, 7
LESSON 31
Previously you compared shapes and put them into groups. In this lesson you will learn how to group quadrilaterals. Use what you know to try to solve the problem below.
A rhombus is one kind of quadrilateral . A rectangle is another kind of quadrilateral . How are a rhombus and a rectangle the same? How are they different?
rhombus rectangle
TRY IT
DISCUSS ITAsk your partner: Can you explain that again?
Tell your partner: I knew . . . so I . . .
Math Toolkit• geoboards• rubber bands• grid paper• index cards• sticky notes
How are a rhombus and a rectangle alike? How are they different?
2 LOOK AHEADA quadrilateral is a shape with 4 sides and 4 angles. The shapes to the right are quadrilaterals. You can name a quadrilateral based on its attributes. An attribute is a way to describe a shape.
a . A quadrilateral is a parallelogram if it has the attributes both pairs of opposite sides are the same length and opposites sides are parallel. Sides are parallel if they are always the same distance apart.
Circle the parallelograms:
b . A quadrilateral is a rectangle if it has 4 right angles. A rectangle also has 2 pairs of opposite sides that are parallel and the same length.
Circle the rectangles:
c . A quadrilateral is a rhombus if it has 4 sides that are all the same length. A rhombus also has 2 pairs of parallel sides.
Circle the rhombuses:
3 REFLECTList 3 attributes a quadrilateral could have.
2 Circle the parallelograms. What other word above describes your circled shapes?
1 Think about what you know about quadrilaterals. Fill in each box. Use words, numbers, and pictures. Show as many ideas as you can.
Word In My Own Words Example
quadrilateral
attribute
parallelogram
rectangle
rhombus
Prepare for Classifying Quadrilaterals
LESSON 31 SESSION 1
Lesson 31 Classify Quadrilaterals692
LESSON 31 SESSION 1
3 Solve the problem. Show your work.
A parallelogram is one kind of quadrilateral . A square is another kind of quadrilateral . How are a parallelogram and a square the same? How are they different?
CONNECT ITNow you will use the problem from the previous page to help you understand how to compare quadrilaterals .
1 What is an attribute of a square that is not an attribute of every rectangle?
2 Does every rectangle have all the attributes of a square?
3 Does every square have all the attributes of a rectangle?
4 Is every square a rectangle? Explain why or why not.
5 Is every rectangle a square? Explain why or why not.
6 REFLECTLook back at your Try It, strategies by classmates, and Picture It and Model It. Which models or strategies do you like best for comparing quadrilaterals? Explain.
CONNECT ITNow you will use the problem from the previous page to help you understand how to name and draw quadrilaterals by looking at their attributes .
1 What is the name of the shape described on the previous page? How do you know?
2 Look at the shape to the right. Is it a quadrilateral? Explain why or why not.
3 Is the shape a parallelogram? Is it a rectangle? Is it a rhombus? Explain.
4 Draw a different quadrilateral that is NOT a parallelogram, a rectangle, or a rhombus.
5 REFLECTLook back at your Try It, strategies by classmates, and Model It and Solve It. Which models or strategies do you like best for naming and drawing quadrilaterals? Explain.
Apply ItUse what you just learned to solve these problems .
6 Circle all the quadrilaterals below that have 2 pairs of sides the same length, but are not rectangles.
7 Draw a quadrilateral that has at least 1 right angle, but is not a rectangle.
8 Draw a quadrilateral in which all sides are not the same length, opposite sides are the same length, and there are no right angles. Then name the quadrilateral.
Study the Example showing how to name a quadrilateral . Then solve problems 1–9 .
ExampleJustin is drawing a quadrilateral with opposite sides that are the same length. All 4 sides are not the same length. What quadrilaterals can Justin draw?
Make a drawing to see what the quadrilaterals might look like.
Opposite sides are the same length. The shape has 4 right angles.
Opposite sides are the same length. The shape has no right angles.
Justin can draw a rectangle or a parallelogram.
Use the shape on the right to answer problems 1–5 .
1 One wall of a shed looks like the shape on the right. How many sides and angles does the shape have?
2 How many parallel sides does the shape have?
3 How many right angles does the shape have?
4 Does the shape have 2 pairs of sides the same length?
5 Circle all the words you can use to name this shape.
Use the clues and shapes A–E to solve problems 6–8 .
6 I have 4 sides. I am a parallelogram. I have all right angles. I am not a square.
I am shape .
I am a .
7 I am a quadrilateral. I do not have any right angles. My sides are all the same length.
I am shape .
I am a .
8 I have more than 1 right angle. Some of my sides are the same length. I am not a quadrilateral.
I am shape .
I am a .
9 Draw a quadrilateral that has at least 3 right angles, 2 pairs of parallel sides, and all sides the same length. Write all of the possible names for your shape. Tell why the names fit.
Complete the Example below . Then solve problems 1–9 .
EXAMPLEA patio has 2 pairs of sides that are the same length . All sides are not the same length, but it does have 4 right angles . What shape is the patio?
Look at how you could show your work using a model.
Solution
Apply it1 Draw a quadrilateral that has no sides the same length and no
right angles. Show your work.
Refine Classifying Quadrilaterals SESSION 4
PAIR/SHAREHow else could you model the shape?
The student used a geoboard to model the shape. Now you can see what the shape looks like.
The shape you draw will not be a rectangle or a square. It will not be a parallelogram or a rhombus.
PAIR/SHAREWhat is a different shape you can draw to solve the problem?
4 A rhombus must have all of these attributes except which one?
A 4 sides that are the same length
B 2 pairs of parallel sides
C 4 right angles
D 4 sides and 4 angles
5 What is the best name that describes all the shapes below?
6 Use the grid below. Draw a quadrilateral that belongs to at least two of these groups: parallelogram, rectangle, or square. Explain why your shape belongs to these groups. Show your work.
7 Use the grid below. Draw a quadrilateral that does NOT belong to any of these groups: parallelogram, rectangle, or square. Explain why your shape does not belong to any of these groups. Show your work.
8 Tell whether each sentence is True or False.
True False
All rhombuses are quadrilaterals. A B
All rectangles are squares. C D
All parallelograms are rectangles. E F
All quadrilaterals are parallelograms. G H
All squares are rhombuses. I J
9 MATH JOURNALJess says that a square cannot be a rectangle because a rectangle has 2 long sides and 2 short sides. Is he correct? Explain.
SESSION 4
SELF CHECK Go back to the Unit 6 Opener and see what you can check off.
equal areas. Express the area of each part as a unit fraction of the whole.
SMP 1, 2, 3, 4, 5, 6, 7
LESSON 33
You have learned about equivalent fractions, equal parts of shapes, and finding area. In this lesson you will learn how to break apart shapes into parts with equal area. Use what you know to try to solve the problem below.
Use different ways to break each square into two equal parts . Shade one part of each square . What unit fraction could you use to describe the shaded part? Explain how you know .
TRY IT Math Toolkit• unit tiles• grid paper• dot paper• sticky notes• fraction models
DISCUSS ITAsk your partner: Why did you choose that strategy?
Tell your partner: The strategy I used to find the answer was . . .
SESSION 1
Explore Partitioning Shapes into Parts with Equal Areas
Explain how you know the unit fraction that names the shaded part of each square.
2 LOOK AHEADYou can break apart the same shape into equal parts in a lot of ways. You can use fractions to describe the area that each part covers. Look at the rectangles below. The shaded areas of all four rectangles are both alike and different.
A B C D
a . What fraction of the area of rectangle A is shaded?
What fraction of the area of rectangle B is shaded?
What fraction of the area of rectangle C is shaded?
What fraction of the area of rectangle D is shaded?
b . For rectangles C and D, what unit fraction is equivalent to the fraction shown
by the shaded parts?
3 REFLECTWhat is the same about the areas shown by the shading in the four rectangles above? What is different?
Use different ways to break each square below into four equal parts . Shade one part of each square . What unit fraction could you use to describe the shaded part? Explain how you know .
CONNECT ITNow you will use the problem from the previous page to help you understand how to divide shapes into equal parts .
1 How many equal parts are on the paper? How many in 1 row?
Suppose Brett colors 1 row. What fraction of the paper does he color?
What fraction of the paper is NOT colored?
Use ,, ., or 5 to compare the fraction of the paper that is colored and the
fraction that is not colored. 2 ·· 8 6 ·· 8
2 What fraction of the paper is 1 row? Explain.
3 Does Brett color 1 ·· 4 of the area of the paper? Use your answers above to explain.
4 How else could Brett have colored 1 ·· 4 of the paper?
5 To color 1 ·· 4 of the paper, must Brett color parts that are next to each other? Explain.
6 REFLECTLook back at your Try It, strategies by classmates, and Model It and Solve It. Which models or strategies do you like best for dividing shapes into equal parts? Explain.
ExampleBrad and Linda each cover a same-sized board with mosaic tiles. Here are the designs they made. What part of Brad’s design is red tiles? What part of Linda’s design is red tiles?
Brad’s Design Linda’s Design
Brad’s Design Linda’s Design
2 rows of 4 tiles 5 8 tiles 4 rows of 2 tiles 5 8 tiles
4 ·· 8 , or 1 ·· 2 , of the tiles are red. 4 ·· 8 , or 1 ·· 2 , of the tiles are red.
Study the Example showing how to divide rectangles into equal parts . Then solve problems 1–10 .
1 How many equal parts are in rectangle A?
2 How many rows are in rectangle A?
3 What fraction of the total area of rectangle A is shaded?
4 Use rectangle B to show another way to divide a rectangle into
6 equal parts. What unit fraction is each part?
5 What fraction of the total area of rectangle C is shaded? Tell how you know.
Refine Partitioning Shapes into Parts with Equal Areas
Complete the Example below . Then solve problems 1–8 .
EXAMPLEA rectangular game board is divided into same-sized squares . There are 4 rows . Each row has 2 squares . What fraction of the total area of the game board does each row cover?
Look at how you could show your work using a model.
1 row out of 4 rows is shaded.
Solution
Apply it1 The triangle is divided into equal parts. How does the area of
one part compare to the area of the whole triangle? Shade 1 ·· 2
of the triangle.
Solution
How many smaller triangles are there?
PAIR/SHAREHow could you solvethe problem withoutusing a model?
PAIR/SHAREWhat is a different way to shade 1
··
2 of the triangle?
The student used a grid to make a model of the game board.
2 Shade 1 ·· 3 of the circle below. How many same-sized parts cover 1 ·· 3
of the circle? Show your work.
Solution
3 A rectangle is equally divided into 2 rows. Each row is divided into 3 same-sized squares. What fraction of the total area of the rectangle is each square?
A 1 ·· 2
B 1 ·· 3
C 1 ·· 4
D 1 ·· 6
Ben chose A as the correct answer. How did he get that answer?
PAIR/SHAREWhat fraction of the whole circle is each part?
PAIR/SHAREWhat do you think Ben was thinking when he chose his answer?
7 Divide each octagon into 4 equal parts. Then shade one or more parts of each to show two different unit fractions. Write the fraction under each octagon. Then compare the fractions using ,, ., or 5.
8 MATH JOURNALSuppose you divide a hexagon into 6 equal parts. Explain how you could shade the parts to show three different unit fractions.
SELF CHECK Go back to the Unit 6 Opener and see what you can check off.